WASHINGTON — One of Washington’s permanent parlor games is how much credit or blame a president deserves for the state of the economy. Inevitably, then, the question being asked now is whether Donald Trump or Barack Obama created today’s strong economy. The correct answer is: neither. To the extent that personal responsibility can be assigned, the worthy recipient is Janet Yellen.

In practice, presidents’ influence over the economy is limited. If it were otherwise, we’d live in an economic paradise. Unemployment would always be low, wages would always rise, and recessions would never occur. No one has that kind of power. Presidents and their agencies can’t govern the business cycle.

The obvious qualification to this reality is the Federal Reserve. By regulating the flow of money and credit, the Fed stimulates or retards the economy, though not always in predictable ways. There are regular collisions between what the Fed can actually achieve and what the public thinks it should achieve. Yellen has led it since 2014 but will leave early next year and be replaced by Fed governor Jerome Powell.

Under Yellen, the economy has made huge progress. Here’s the record since she became Fed head in February 2014: Payroll employment has expanded by nearly 10 million jobs; the unemployment rate has dropped from 6.7 percent to 4.1 percent; average hourly earnings, uncorrected for inflation, rose from $24.32 to $26.55. (Corrected for inflation, the wage gain is about 4 percent — not great but not stagnation either. The pace, if maintained, would be roughly 10 percent over a decade.)

None of this was preordained. It’s true that Yellen followed the policies of her predecessor, Ben Bernanke, but these policies were not, as Yellen has repeatedly stated, on “automatic pilot.” They required much judgment. The problem faced by Yellen was to maintain a policy of easy money long enough to promote the economy’s recovery but not so long as to feed either inflation or financial speculation.

It will be some years before a final verdict can be rendered on Yellen’s stewardship. Is the stock market overvalued? Did the Fed contribute to that? What happens if stocks crash? Questions linger.

Still, for the moment, most of Yellen’s judgments seem on the mark. Bernanke’s Fed had adopted a policy of ultra-easy money. It had reduced short-term interest rates to near zero and, in an effort to bring down long-term rates, had purchased more than $3 trillion of Treasury and home-mortgage securities. (When the Fed buys securities, their price typically goes up and their interest rate goes down.)

Yellen has slowly been reversing this policy. Since December 2015, the Fed has raised short-term interest rates five times, including an increase last week. The so-called Fed funds rate has risen to a maximum of 1.5 percent. More increases are expected in 2018. Likewise, the Fed is reducing its holdings of Treasury and mortgage securities, putting upward pressure on long-term interest rates.

All this has gone smoothly — and that’s just the point. It wasn’t inevitable. The mechanics of raising interest rates from their ultra-low position involved new and untested procedures. There were dire predictions that things would go awry. They didn’t.

“The Fed was acutely aware that it had to be perceived as successful … to have public support,” says economist Ken Matheny of Macroeconomic Advisers.

Given her reputation as a conciliator, Yellen may also have improved the Fed’s public standing. Remember: The chair can’t single-handedly impose policy. The Fed’s key decision-making body, the Federal Open Market Committee (FOMC), has 12 members. Despite a tradition of deference to the chair, “you have to achieve a consensus,” says Matheny. “It’s not a dictatorship.”

Yellen leaves a solid legacy, built on professional competence, integrity and dignity.

Just what prompted President Trump to pass her over in favor of Powell is unclear. It’s not monetary policy, where both adhere to the present Fed consensus.

Trump’s decision flouts an informal custom, since the 1980s, to reappoint the Fed chair to at least a second four-year term. It may be that the president feels more comfortable with Powell. Or he may think (inaccurately?) that, if the economy weakens, he can more easily bend Powell to his will than Yellen.

Whatever the case, the irony is hard to miss. Powell’s performance, at least initially, will be compared to Yellen’s. It is a high hurdle to clear.